ESA GNC Conference Papers Repository

Control Moment Gyro (CMG) clusters are common technologies used to control the attitude of rigid satellites. A single-gimbal CMG is composed of a flywheel rotating at a constant speed and of a gimbal which can spin the axis of rotation of the flywheel, creating a gyroscopic torque. The main advantages of this actuator over the reaction wheels are their power-efficiency, the speed and precisions of the maneuvers created. Nevertheless, they are more difficult to steer because of the presence of singularities. Indeed, some values of the gimbal angles (angles of rotation of the flywheel axis) make it impossible for a cluster of CMGs to create a torque around an axis. Finding a steering law for a cluster of CMGs belongs to the classical problems of finding a guidance law for redundant, non-linear systems in presence of singularities, and is still studied (see [1]). The goal of this steering law is to divide the total required torque among the actuators, while the number of actuators is greater than the number of variables to control. Mathematically, it comes down to inverting a rectangular matrix that can be rank-deficient, and under constraints like saturations. Other typical requirements are the real-time feature of the algorithm and the capability of handling failures of CMGs in the cluster or even to be adapted to different cluster configurations ([2]). The approach proposed in this paper is to use the extended Kalman filter formalism with a new formulation of the kinematic equations of the cluster. This formulation gives well-conditioned mathematical expressions and helps avoiding the singularities. However, this benefit is compensated by the introduction of other constraints in the problem, which is why the extended Kalman filter is used to perform a quadratic optimization. Other constraints can be added in the filter, like saturation. The importance of the constraints can be varied according to the needs; therefore the law can act as a priority-based controller [3]. In addition, it presents stability proofs that are detailed in the papers [3] and [4]. Tuning this steering law can be challenging because of the presence of singularities and of the stability conditions. The off-line tuning of the steering law based on genetic algorithms is presented in the paper. The simulation results, during typical maneuvers to assess the feasibility and performance when encountering singularities, are also detailed. The study case considers a cluster of six control moment gyros in a pyramidal isotropic position. Also, failures of one, two or even three CMGs are simulated and the steering law can be adapted by only changing the gains, not its structure.